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Singular coverings and non‐uniform notions of closed set computability
Author(s) -
Le Roux Stéphane,
Ziegler Martin
Publication year - 2008
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200610058
Subject(s) - computability , mathematics , computable analysis , lebesgue measure , set (abstract data type) , point (geometry) , measure (data warehouse) , lebesgue integration , pure mathematics , discrete mathematics , combinatorics , computer science , geometry , database , programming language
The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskiĭ, Tseĭtin, Kreisel, and Lacombe have asserted the existence of non‐empty co‐r. e. closed sets devoid of computable points: sets which are even “large” in the sense of positive Lebesgue measure. This leads us to investigate for various classes of computable real subsets whether they always contain a (not necessarily effectively findable) computable point. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)